Answered

How does the graph of g(x)=4⌊x⌋ differ from the graph of f(x)=⌊x⌋?




Multiplying by 4 shifts the graph of ​ g(x)=4⌊x⌋ up 4 units.


Multiplying by 4 shifts the graph of ​ ​ g(x)=4⌊x⌋​ down 4 units.


Multiplying by 4 shifts the graph of ​ g(x)=4⌊x⌋ ​ ​right 4 units.


Multiplying by 4 stretches the graph of ​ ​ g(x)=4⌊x⌋ vertically by a factor of 4

Verified Answer :

multiplying by 4 stretches the graph of g(x)4[x] vertically by a factor of 4

Answer:

The correct option is D) Multiplying by 4 stretches the graph of ​ ​ g(x)=4⌊x⌋ vertically by a factor of 4

Step-by-step explanation:

Consider the provided graph.

Transformation:

  1.  The graph of parent function f(x) move up b unit for f(x)+b.
  2. The graph of parent function f(x) move down b unit for f(x)-b.
  3. The graph of parent function f(x) move left b unit for f(x+b).
  4. The graph of parent function f(x) move right b unit for f(x-b).
  5. For the given function f(x) the new function g(x) = a f(x) will stretch vertical by factor a if a>1  
  6. For the given function f(x) the new function g(x) = a f(x) will compressed vertical by a factor of a if 0<a<1

Now consider the provided graph of g(x)=4⌊x⌋

The parent function is f(x)=⌊x⌋

The new graph is multiplied by 4 which is grater than 1.

Thus, the graph of the function will stretches vertically by a factor of 4.

Hence, the correct option is D) Multiplying by 4 stretches the graph of ​ ​ g(x)=4⌊x⌋ vertically by a factor of 4

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